Absolute encoder employing linked sub-encoders and beat track

ABSTRACT

An absolute encoder employs multiple sub-encoders of different resolutions and a linking algorithm for combining the sub-encoder outputs to form an accurate, high-resolution position estimate. The sub-encoders can utilize edge modulation of a main grating track, sloped patterns of successively higher periods, and other types of scale patterns. The sub-encoders can also use a variety of detector types suitable for the patterns being used. In one linking approach, pairs of tracks are linked together successively by applying a phase shift to the coarser track and then combining it with the finer track such that the transitions of the coarse track estimates become aligned with those of the finer track, whereupon the values can be combined to form a linked position estimate. In another approach, beat tracks are calculated from physical tracks of similar period, and the beat tracks are used as the coarser tracks in the linking process.

CROSS REFERENCE TO RELATED APPLICATIONS

This Patent Application is a Divisional of U.S. patent application Ser.No. 10/990,769 filed on Nov. 17, 2004 now U.S. Pat. No. 7,253,395entitled, “ABSOLUTE ENCODER EMPLOYING CONCATENATED, MULTI-BIT,INTERPOLATED SUB-ENCODERS”, and also claims priority under 35 U.S.C. §119(e) of U.S. provisional patent application 60/520,926 filed Nov. 17,2003, the disclosure of both of these applications being herebyincorporated by reference in their entirety.

BACKGROUND

The present invention is related to the field of position encoders.

Position encoders can be incremental or absolute. A sensing unit of anincremental encoder senses position within an individual cycle betweentwo scale graduations, but has no information about which cycle of thescale is being read. Typically, incremental encoder sensing units arecombined with electronics to perform up/down counting of scale cycles.Thus, once an initial point on the scale has been identified, theencoder system measures displacement along the scale by reference to theup/down counters. Incremental encoders may not be useful in manyapplications, because any interruption in the inputs invalidates thedisplacement estimate in the counters. For example, if the scale isobscured at any point (perhaps by dirt), the counters will not registerthe proper value on the far side of the obscuration. Similarly, in thecase of a power interruption, the encoder has no information about scalemotions during the interruption. In either case, it is necessary toperform some initialization procedure to re-establish the encoder'sreference.

Some incremental encoders employ an index, or reference, mark built intothe scale. A separate sensing mechanism is usually required to detectthe passing of the index mark. The index mark is typically used to resetthe counters to a predetermined value, such as zero. However, this resetcan only be effected by purposely moving the scale to force the indexmark to pass the sensing mechanism.

In contrast to incremental encoders, absolute encoders employ sensingunits that generate a complete or “absolute” position indication foreach point on the scale without the need to count scale cycles as thescale moves. Absolute encoders do not require a position history, suchas provided by a counter, and consequently their position indicationsare not invalidated by power interruptions or other events that requirere-referencing an incremental encoder.

A classic approach for relatively low resolution absolute encodersincorporates multiple code tracks, each successive track being a factorof 2 more coarse. Thus, if there are 2^(N) cycles in the scale, thereare N tracks, which, when taken together, provide an N-bitcycle-identifying word. In one variation, Gray encoding is used toensure that the code values change monotonically with movement of thescale.

Recently, a pseudo-absolute encoder has been introduced in which acycle-identifying code is spread out over several cycles. If there are2^(N) cycles on the scale, the N bits of the code are spread over Nadjacent cycles. Thus, to uniquely identify any particular cycle, thebit value at the current cycle is combined with the bits from theimmediately adjacent N−1 cycles, which must have been sensed andremembered. The cycle-identifying code is a pseudo-random chain code,which means that the sequence of bits along the entire length of thecode is such that, taken N bits at a time, no sequence repeats over the2^(N) cycles and each adjacent N-bit code word has the same bit sequenceas its neighbor, except for either the left-most or right-most bit inthe pseudo-random position word, and that the other N−1 bits are rightor left shifted respectively.

Yet another approach to building an absolute encoder is taught in U.S.Pat. No. 5,965,879. The incremental scale and associatedcycle-identifying code are imaged onto a 2-dimensional array detector,such as a CCD. The thus captured image is processed using imageprocessing algorithms that mimic the way a human would read a ruler. Oneportion of the algorithm tracks the relative position of the incrementalscale's lines as they move across the field of view, while the secondportion of the algorithm interprets the cycle-identifying code. Theoutput of the combined algorithm is the absolute displacement in theform: “the Mth cycle is 10 microns from the edge of the field, so theabsolute displacement is M*P+10 microns, where P is the period of thescale”.

Yet another class of absolute encoders uses multiple periodic scaletracks with no explicit cycle-identifying code. These encoders areexemplified by U.S. Pat. No. 6,366,047. These encoders employ a numberof fine tracks of similar period. The fine tracks are combinedalgebraically to form “beat” tracks of lower spatial frequency (orlonger spatial period). The beat tracks are used to identify coarseposition along the scale, which can be combined with positioninformation from one of the fine tracks to arrive at an overall absoluteposition indication.

SUMMARY

Each of the above absolute encoders suffers from drawbacks. The basicN-track approach becomes unwieldy (physically large) for high resolutionsystems (N large) and is difficult to align. The code-spreadingapproach, in which the information in the N tracks is effectively codedinto the single track, must be jogged for several cycles before it knowswhere it is after a signal loss. The approach of the '879 patent islimited in frame rate by the image processing engine, and themulti-track approach of the '047 patent can experience significanterrors due to an inherent magnification of errors in any of the finetracks. An absolute encoder that avoids these disadvantages would bedesirable.

Disclosed is an absolute encoder with a multi-track scale including atleast two periodic tracks which are algorithmically linked to enable theencoder to generate high-precision absolute position estimates. Theperiod of a first track is exceeded by the period of a second track by atrack ratio, and the tracks have a phase relationship with a certainmagnitude of uncertainty. For example, the relative phase between thetwo tracks may vary by plus or minus one-quarter of a cycle of the firsttrack. This phase variation may arise due to grating runout,eccentricity (in rotary encoders), and misalignment, among other things.

Detector circuitry in the encoder is operative in response to periodicenergy patterns from the tracks to generate corresponding sets of analogsignals, the analog signals within each set representing amplitudes ofthe corresponding energy pattern at respective predetermined spatiallocations. In the disclosed optical encoder, the detector circuitryincludes photodetectors. In encoders based on other sensing technology,such as magnetics, the scale and detector circuitry will be realized byanalogous magnetic components.

Processing circuitry in the encoder is operative in response to the setsof analog signals to perform a track linking process, which is amathematical algorithm that transfers all of the accuracy and resolutionof the first track to the second track. As an initial step, first andsecond position estimates are generated. The first position estimaterepresents a position sample of the first track modulo the first trackperiod. The second position estimate represents a position sample of thesecond track modulo the second track period and scaled with respect tothe first position estimate to account for the track ratio. The secondposition estimate has sufficient resolution that a least significantpart of the second position estimate overlaps a corresponding mostsignificant part of the first position estimate by at least a minimumoverlap amount, which is determined by the magnitude of uncertainty ofthe phase relationship between the first and second tracks. In anexemplary embodiment, both the first and second tracks are interpolatedto 10 bits of resolution, and the least-significant five bits of thesecond track position estimate overlap the most-significant five bits ofthe first track position estimate. That is, the least-significant fivebits of the second track position estimate represents the position ofthe second track over a range and to a resolution that are the same asthe range and resolution of the first track position represented by themost-significant five bits of the first track position estimate. In suchan embodiment, the uncertainty of the phase relationship between thefirst and second tracks may be as high as about 0.94 of the period ofthe first track.

The first position estimate is then subtracted from the second positionestimate to create a corrected second position estimate. Thissubtraction is accompanied by filtering or smoothing that eliminatesphase noise present in the original second position estimate. Also, aphase adjustment may be included to account for an average phase offsetbetween the two tracks. As a result of these operations, thesample-to-sample transitions of the most-significant part of thecorrected second position estimates become precisely aligned with theperiod-to-period transitions of the first position estimates.Consequently, the two values can be combined readily (e.g., byconcatenation) to form a position estimate representing the position ofthe scale modulo the second track period but to a higher resolution thatincludes the full resolution of the first position estimate.

The above linking process can be repeated for additional tracks toextend the range of position measurements provided by the encoder. Inone class of encoders, the linking is simply repeated, each time usingthe result of the last iteration and a next successive track. Forexample, if a third track were included, it would be linked with thelinked track resulting from the above linking process of the first twotracks. The linking could be accomplished in exactly the same fashion asdescribed above. It will be appreciated that each track will have asuccessively greater period, and the final track will typically have aperiod greater than or equal to the overall length of the scale (or, ina rotary application, greater than or equal to the circumference of theannular scale).

Another class of encoders employ what are referred to as “beat tracks”,which are mathematical tracks created by performing a subtractionbetween position estimates of tracks having distinct but generallysimilar periods. In such encoders, beat tracks of greater period can becreated by proper selection of the periods of the tracks from which thebeat tracks are created. For example, if two tracks having periods of500 microns and 520 microns are beat together, a beat track having aperiod of 13 mm can be created. The position estimates of a beat trackare generated from the position estimates of the tracks from which thebeat track is created. Thus, if a beat track is created from two tracksthat have both been linked to a fine track, the beat track can be linkedto one of the tracks. The use of the mathematical beat tracksadvantageously avoids the need for physical tracks of long period on thescale, which can be difficult to sense with a physically small detector.Additionally, because the beat tracks are all linked to the same finetrack, they do not suffer the error-magnification problem of priorencoders employing the beat principle, and therefore can achieve greateraccuracy.

Each individual track, when combined with the source that illuminates itand the detector that senses its fringes, constitutes an incrementalencoder. For convenience, these track/sensor combinations are referredto herein as “subencoders”. Several alternative embodiments for thesesubencoders are shown. For example, in one embodiment, the scaleincludes a 50:50 duty cycle grating, wherein the alternating lines ofthe grating are either transmissive/opaque, reflective/non-reflective,or phase delaying/non-phase delaying. The lines of the grating areoriented parallel to the cross-track direction and are positioned nextto each other in the along-track direction. In the disclosed absoluteencoder, a subencoder of this first type is employed as the highestresolution or “fine” position subencoder.

In a second subencoder embodiment, the scale includes a diagonalgrating, which is a striped pattern slanted relative to the cross-trackdirection. When such a rotated grating pattern is translated in thealong-track direction, the dark and light lines of the striped patternappear to move in a cross-track direction, similar to the effect of abarber pole. Along-track scale motion is determined by detecting thecross-track stripe displacement.

In another embodiment, a subencoder scale is created by tailoring one orboth of the along-track edges of a grating, such as the grating for thefine track. Position information is derived by intentionally varying thecross-track dimension of a grating track according to a periodicfunction of the along-track position. For example, the edge of the trackmay vary as a sawtooth or sinusoid function.

Other subencoder embodiments include the use of an cylindricaldiffractive optical element (DOE) extended in the along-track directionand whose cross-track position varies periodically as a function of thealong-track position. This DOE generates a focused line of lightextending in the along-track direction, and the focused line of lightmoves in the cross-track direction with the same periodic function asthe scale moves with respect to the detector. An alternative scale has aperiodic array of cylindrical diffractive optical elements oriented withtheir diffracting power in the along-track direction, such that each DOEwhen illuminated forms a focused line of light extending in thecross-track direction. This line of light moves in the along-trackdirection as the scale moves. This type of optical pattern can be sensedby a detector having a response that varies sinusoidally in thealong-track direction, an example of which is shown below.

Each of the subencoder embodiments further includes a suitablyconfigured detector, disposed to detect the optical pattern changes thatoccur as the scale is displaced in the along-track direction.Additionally, each of the subencoder embodiments in which cross-trackscale displacements cause an observable optical pattern changepreferably includes a cross-track reference track. This reference trackis preferably designed to be insensitive to along-track displacements.

For convenience, the invention is described herein in terms of a linearposition sensor. However, those skilled in the art will understand thatthe principles apply equally well to rotary position sensors, where thealong-track direction is understood to be around the circumference of anannular scale and the cross-track direction is understood to be theradial direction.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features and advantages of theinvention will be apparent from the following more particulardescription of preferred embodiments of the invention, as illustrated inthe accompanying drawings in which like reference characters refer tothe same parts throughout the different views. The drawings are notnecessarily to scale, with emphasis instead being placed uponillustrating the embodiments, principles and concepts of the invention.

FIG. 1 is a schematic diagram of an optical encoder in accordance withthe present invention;

FIG. 2 is a waveform diagram depicting signals in the optical encoder ofFIG. 1;

FIG. 3 is a diagram showing a portion of an optical scale in the opticalencoder of FIG. 1;

FIG. 4 is a flow diagram showing generally how position calculation isperformed in the optical encoder of FIG. 1;

FIG. 5 is a diagram of a multiple-track (or multiple-grating) scaleusable in the optical encoder of FIG. 1;

FIG. 6 is a diagram of a first multiple-element detector usable in theoptical encoder of FIG. 1;

FIG. 7 is a diagram of a second multiple-element detector usable in theoptical encoder of FIG. 1;

FIG. 8 is a diagram of an alternative multiple-track scale usable in theoptical encoder of FIG. 1;

FIG. 9 is a diagram of a multiple-element detector usable with the scaleof FIG. 8;

FIG. 10 is a diagram of yet another alternative multiple-track scaleusable in the optical encoder of FIG. 1;

FIG. 11 is a diagram illustrating an optical encoder employing a gratingwith a sinuous pattern;

FIG. 12 is a flow diagram illustrating the general operation of amultiple-track absolute encoder such as the encoder of FIG. 1;

FIG. 13 is a waveform diagram showing waveforms of interest in anencoder employing multi-track linking as depicted in FIG. 12;

FIG. 14 is a flow diagram illustrating how position estimates arecombined for multiple tracks in an absolute encoder such as the encoderof FIG. 1;

FIG. 15 is a waveform diagram showing waveforms of interest with respectto the combining process of FIG. 14;

FIG. 16 is a flow diagram illustrating a specific implementation of thecombining process of FIG. 14;

FIG. 17 is a waveform diagram showing waveforms of interest in anencoder employing the implementation of FIG. 16;

FIG. 18 is a waveform diagram illustrating the creation of beat signalsthat can be used in an absolute encoder such as the encoder of FIG. 1;

FIG. 19 is a diagram depicting the relationships among various physicalgrating tracks and beat tracks in one embodiment of an absolute encoder;

FIG. 20 is a flow diagram illustrating a process for realizing beattracks in the scheme of FIG. 19 and a final resulting positionindication;

FIG. 21 is a waveform diagram showing how a rollover calculationcondition is corrected in the process of FIG. 20;

FIG. 22 is a diagram depicting the relationships among various physicalgrating tracks and beat tracks in another embodiment of an absoluteencoder; and

FIG. 23 is a diagram showing the use of virtual fine tracks in a schemelike that of FIG. 22 to realize a non-integer relationship between twotracks.

DETAILED DESCRIPTION

In FIG. 1, sensor apparatus 10 is installed as part of a reflective,diffractive optical encoder. A source 12 illuminates a scale 14 on whicha set of periodic, reflective diffraction gratings or tracks 16 havebeen created. Light from the source 12 is reflectively diffracted fromthe scale 14 toward the sensor apparatus 10, which in the illustratedembodiment includes an optical detector 18. The diffraction grating 16generates multiple orders of diffracted light which interfere with eachother to form optical fringe patterns (not illustrated) on the detector18. The samples from the detector 18 are sent to an electronic processor20 which uses the samples to calculate fringe phases for each track.

Each fringe pattern is ideally a sinusoid characterized by a period P.Conceptually, when the scale 14 moves laterally relative to the detector18 along the direction indicated by line 22, the fringe pattern moves aproportional distance on the face of detector 18. An accuratemeasurement of the changes in the phase of the fringe pattern is aproportional measurement of the movement of the scale 14.

For ease of reference, a set of coordinate axes 24 are shown to indicatedirections of interest. The direction of motion 22 lies along the Xaxis. The scale 14 lies in a plane extending in the X and Y directions,with the individual elements of the gratings 16 extending in the Ydirection. The scale 14 and the sensor apparatus 10 are separated in theZ direction. It will be appreciated that the interference fringe patternincident on the detector 18 extend in both the X and Y directions, withthe grating-created intensity variations in the X direction and atypical beam profile in the Y direction (i.e., a central maximum andgradually lower intensity going outward along the Y axis).

FIG. 2 illustrates, for one embodiment, the creation of position-varyingsignals by the sensor apparatus 10 as its X-axis position relative tothe scale 14 changes for a single grating 16 on the scale. The signalscan be generated by a technique referred to as “4-bin” sampling, due toits use of four sampling locations separated by ¼ of a fringe period.The sensor apparatus 10 generates first and second quasi-sinusoidalsignals 26, 28 by sampling within an optical fringe at locationsseparated by ¼ of a fringe period or 90 degrees. The term“quasi-sinusoidal” is used because of various known non-idealities inany encoder implementation—the signals are ideally purely sinusoidal andseparated by precisely 90 degrees. One signal (such as signal 26) isdenoted the sine (SIN) signal, and the other (such as signal 28) isdenoted the cosine (COS) signal. The selection is somewhat arbitrary,and can be made based on which direction of motion is to be denoted the“positive” versus the “negative” direction. It will be appreciated thatthe sensor apparatus 10 may be configured to sample the optical patternat other spatial locations, for example at locations separated by ⅓ of afringe period or other sub-multiples of a fringe period.

The analog SIN and COS signals 26 and 28 are sampled byanalog-to-digital conversion circuitry (not shown) within the processor20, and an arctangent (ARCTAN) signal 30 is calculated from theresulting digital values. The ARCTAN signal 30 has a rampcharacteristic, rising linearly (ideally) from a minimum to a maximumover one fringe cycle. Thus, the amplitude of the ARCTAN signal isproportional to the perceived relative position of the sensor 10 and thescale 14 within a given fringe period. The calculation that results inthe ARCTAN signal 30 is often referred to as “interpolation”. Forexample, “10-bit interpolation” means that the relative position betweenthe sensor 10 and the scale 14 within a given fringe period is known(ideally) to a resolution of 2⁻¹⁰, or approximately to one part inone-thousand. It will be appreciated that the smooth-profile ramp signal30 of FIG. 2 is actually an approximation of a signal having 1,024-levelquantization in such a system.

Signals of the type shown in FIG. 2 are commonly used in the industry,and may be utilized in encoders according to the present invention. Ingeneral, however, the presently disclosed techniques may be used withalternative types of signals. For example, an alternative sensor maygenerate a ramp signal such as ramp signal 30 directly, without anycalculation of intermediate SIN and COS values.

FIG. 3 illustrates the general configuration of the optical gratings ortracks 16 on the scale 14. A first track of very fine pitch is referredto as the fine track FT. A typical pitch for track FT is 20 microns, forexample. Two tracks of relatively coarser pitches are shown as tracksCT1 and CT2. Specific examples of coarse tracks are given below. It willbe appreciated that FIG. 3 is for general illustrative purposes only;specific embodiments (examples of which appear below) may have only onecoarse track or may have three or more coarse tracks, depending in parton the length of the scale 14. Another factor is whether or not thetechnique of “beat tracks”, described below, is used.

In general, the tracks FT, CT1, CT2 . . . are used to provide anindication of absolute position at each point of the scale, in contrastto incremental encoders that provide an indication of position within afringe and rely on either an internal or external counter to keep trackof fringe crossings. Generally, the fine track FT provides theleast-significant portion of the position estimate, and the coarsertracks provide the most-significant portion. The most-significant andleast-significant values are combined to form a single, high-resolutionnumber representing absolute position.

This process is illustrated more formally in FIG. 4. At step 32, theARCTAN is calculated for each of the tracks, to a resolution of 10 bitsfor example. Example outputs labeled NUM1-NUMn are shown for the finetrack FT and successive coarse tracks CTn. At step 34, these values areused in a “linking” process that links the values from the differenttracks together so as to form a single output. In FIG. 4, this output isshown as having concatenated components [CTn][CTn−1] . . . [FT]. Anexample is shown as NUM4, which is a 20-bit value having 10 bits fromtrack FT, 5 bits from track CT1, and 5 bits from track CT2. As describedbelow, the linking process of step 34 is substantially more complex thansimply picking corresponding bits from the various track outputs, due tothe inherent imprecise alignment of the tracks with respect to eachother. Rather, the more significant components of the final positionestimate are arrived at by a process of phase-adjustment and smoothing,as described in more detail below.

FIG. 5 shows a set of grating tracks including a fine track 44 andcoarse tracks 36, 38 and 40 (not to scale). The coarsest track 36 has aperiod that equals the full range of the encoder (in a rotaryapplication, coarse track 36 has a period of 2π radians), and theremaining tracks have periods that are some fraction of the period ofcoarse track 36. The period and interpolation level of the fine track 44ultimately determine the resolution of the encoder. The fine track 44has a period of 20 microns. A first coarse track 42 is defmed by aperiodic variation of one edge of the fine track 44. The first coarsetrack 42 has a period of 640 microns, which is 32 times the period ofthe fine track 44. A second coarse track 40 is 32 times more coarse thanthe first coarse track 42, with a period of 20.480 millimeters. A thirdcoarse track 38 is again 32 times more coarse, with a period of 655.360millimeters. FIG. 5 also illustrates a possible fourth coarse track 36,again a factor of 32 more coarse, but its period of 20.97 meters isunlikely to be needed in most applications. Note, however, that coarsetrack 36 could be made with a period that is, for example, 2 timeslonger than the previous track, giving a total encoder range of about1.3 meters.

Additionally, FIG. 5 illustrates an optional reference track 46, whichprovides a measure of the instantaneous cross-track position of thescale 14 relative to the sensor apparatus 10. This cross-trackmeasurement is an aid to initial encoder alignment and provides data tocompensate for cross-track-to-along-track crosstalk inherent in certaintrack designs. This crosstalk is explained below.

The scale 14 may have other optional tracks or features not illustratedin FIG. 5. For example, the scale 14 may include an index mark toprovide a reference point for the encoder that may be aligned to aphysical point on the object whose position is being measured.

As mentioned, the absolute encoder includes a number of separatesubencoders whose outputs are linked to arrive at the full positionoutput. The subencoders operate as independent incremental encodersinsofar as converting optical patterns from the respective tracks on thescale 14 into respective electrical signals indicating relative positionof the subencoder. A light source may be shared by one or moresubencoders.

Subencoder 1: In one embodiment the fine track 44 is an opticaldiffraction grating including alternating striped regions of high andlow reflectance. A typical period for this embodiment is 20 microns. Inone embodiment, this track is illuminated by a spatially coherent lightsource, and the diffracted light is preferably sensed with aninterdigitated phased array detector. The light source may include avertical cavity surface emission laser (VCSEL), and both the VCSELsource and the interdigitated array detector are disposed on a commonsubstrate. Sensor apparatus 10 (FIG. 1) houses the substrate. Theencoder in the '674 published application operates using Talbotinterference, which does not require optical elements disposed betweenthe source/detector and the scale. This configuration permits theseparation between the sensor apparatus 10 and the scale 14 to be on theorder of millimeters; in one typical embodiment the separation is 4.7millimeters.

Subencoder 2: One embodiment for a coarse track subencoder includes thetrack illustrated in FIG. 5 as the first coarse track 42, a VCSELsource, and a so-called 4-bin detector array. As illustrated, the firstcoarse track 42 is formed by modulating the length of the grating linesthat form the fine track 44. In this example, the modulation has aperiod that is 32 times the fine track period, and the amplitude ofmodulation (marked “Ampl” in FIG. 5) is, for example, approximately 0.25millimeters. The modulation function is preferably a sinusoid. Also, theamplitude is preferably less than 50% of the cross-track dimension offine track 44 to limit interference with the operation of the fine track44. In operation, light from the VCSEL illuminates scale 14 and isreflectively diffracted by fine track 44. The light reaching the scale14 at the modulated edge of fine track 44 is diffracted in a complextwo-dimensional pattern that, to first order, retains the sinusoidalmodulation of the edge of the fine track 44.

Referring to FIG. 6, a detector substrate 48 housed within the sensorapparatus 10 includes several photodetectors used in conjunction withthe tracks shown in FIG. 5. The light diffracted by the central portionof the fine track 44 is sensed by a fine track detector array 50, whichis an interdigitated, four-phase array detector. Pads labeled “T0”,“T90”, “T180”, and “T270” make connections with respective sets ofdetector elements that correspond to phases 0, 90, 180 and 270 of aperiod of the detected fringe pattern.

The light diffracted by the first coarse track 42 (FIG. 5) is sensed bya coarse track detector array 52, which is a four-bin array having fourquarter-cycle wide photodetectors 54 arrayed side by side. It will berecalled that the period of the first coarse track 42 is 640 microns forexample. Because there is a diverging cone of light from the VCSELsource, the intensity pattern reaching the sensor apparatus 10 may havea spatial scaling factor of two. In such an embodiment, then, eachquarter-cycle photodetector 54 is preferably 320 microns wide in thealong-track dimension, and has a cross-track dimension more than twicethe amplitude of the modulation function to allow for cross-trackmisalignment. In the illustrated embodiment, the modulation amplitude is100 microns, and the photodetectors 54 are approximately 900 microns inthe cross-track dimension, where again there is a factor of two toaccount for the magnification of the diverging cone of light.

These wide detectors 54 average out the high frequency variations in thecomplex diffraction pattern and produce a signal that approximates thesinusoidal edge modulation that constitutes track 42. Preferably, thedetector width is a multiple of the fine track period to minimizemodulation at the fine track period. The four coarse track detectors 54together produce two quadrature signals that can be processed using wellknown algorithms to produce the relative phase of the sinusoidal edgemodulation.

Subencoder 3: A third coarse track subencoder includes a second coarsetrack 40 (FIG. 5), a VCSEL or LED source, and a quadrature detectorarray. The track 40 is called a sloped grating track, and includes analternating array of reflecting and non-reflecting regions. The arrayforms a periodic pattern that appears as sloped stripes with a 50:50duty cycle. The pattern is characterized by its period λ (lambda) in thealong-track direction, and the stripes' cross-track thickness T. Thestripes are truncated at each end in the cross-track dimension, and thushave a generally parallelogram shape. The pattern may also becharacterized by the slope S of each stripe segment, which is equal to2T/λ. In one embodiment, the track thickness T is 100 microns and theperiod λ is 32 times the period of the first coarse track 42. In theillustrated case, this period is 20.48 millimeters.

FIG. 5 also illustrates additional examples of this type of coarsetrack. A third coarse track 38 has a period of 655.360 millimeters, anda fourth coarse track 36 has a 20.97152 meter period. Many encoderapplications do not require such a long range, and therefore in suchapplications it may be possible to reduce the period and slope of thefourth coarse track or dispense with a fourth coarse track altogether.More generally, for any given application, the number of coarse tracksand their respective periods and slopes are selected as needed.

FIG. 7 illustrates a second detector substrate 64 also housed within thesensor apparatus 10 that contains three detector arrays and is used inconjunction with the sloped grating tracks 40, 38 and 36 to form therespective subencoders. The preferred array is a quadrature shapeddetector (QSD) array 66. The QSD array includes at least one sine shapeddetector 68 and one cosine shaped detector 70. The sine shaped detector68 includes an area photodetector 68A whose sensing area is modulated byat least one cycle of a sinusoid. Preferably, as illustrated in FIG. 7,sine shaped detector 68 further includes a second area photodetector 68Bwhose sensing area is modulated by a sinusoid that is out of phase withrespect to the modulating sinusoid of photodetector 68A by a half cycle.The cosine shaped detector 70 is identical to sine shaped photodetector68 except for the phase of the modulating sinusoid(s); the modulatingsinusoids are shifted by 0.5π with respect to the sine shaped detector68.

The area photodetectors 68A, 68B are modulated in the cross-trackdirection, and the period of the modulating sinusoids is proportional tothe cross-track dimension T of the corresponding sloped grating. In theillustrated embodiment, the modulation period is equal to 4T. One factorof 2 accounts for the optical scaling due to the expanding cone oflight, and the other factor of 2 accounts for the 50:50 duty cycle ofthe pattern.

In operation, the light from the LED or VCSEL illuminates a given coarsetrack 36, 38 or 40. The light reflected from the track, at a distance ofabout 5.2 millimeters in a typical embodiment, forms a pattern of darkand bright regions similar in geometry to the track pattern itself,scaled by a factor determined by the geometry of the expanding cone oflight (typically a factor of 2 when the source and detector array are ina common detection assembly). Along-track motion of these sloped lightstripes, when detected in a narrow, cross-track window, appears as aslower cross-track motion of the light pattern.

When a stripe of light produced by the sloped grating is swept acrosseither shaped photodetector (e.g. 68A/68B) at a constant speed, thephotodetector generates a sinusoidally varying output signal. As withthe detectors described above, the complementary photodetectors (e.g. 68and 70) can be operated differentially to produce a sinusoidal outputsignal having little or no bias offset. Because of their geometry, thesignals produced by shaped detectors 68 and 70 are always 0.5π shiftedin phase.

As illustrated in FIG. 7, the QSD 66 may include additional pairs ofshaped photodetectors, illustrated as detectors 72, 74, to increase thesignal strength and provide averaging to reduce signal errors. The widthof these additional detectors is small relative to the period of thesloped gratings with which they are used. For example, QSD 66 istypically 1000 microns wide while the period of the stripes produced bythe second coarse grating 40 is 40,000 microns in the plane of thedetector. Thus, the slight phase shift introduced between pairs ofdetectors by spreading them out in the along-track direction isnegligible.

Subencoder 4: This subencoder embodiment includes a “repeated indextrack”, a spatially coherent light source, and a suitable index markdetector. FIG. 8 illustrates schematically the fine track 44 and arepeated index track 76. The repeated index track 76 consists of aperiodic array of diffractive optical elements (DOEs) 78, each DOE beingin the form of a short focus cylindrical lens. As illustrated, thenon-powered axis of each DOE 78 is parallel to the cross-trackdirection. Each DOE 78 thus creates a focused (or partially focused)line of light that travels in the along-track direction as the DOEitself moves with the scale 14. The track 76 is called a repeated indextrack because a single DOE 78 can function as an index mark inincremental encoders.

The repeated index track 76 is preferably used with a multi-elementdetector having a sinusoidally varying response in the along-trackdirection, such as the QSD detector array 79 shown in FIG. 9. Thedetector array 79 includes at least two detectors 81 and 83, each havingtwo complementary elements (81A, 81B) and (83A, 83B) having across-track dimension that varies sinusoidally. The detectors 81 and 83are offset from each other by ¼ of a cycle in the along-track direction.As the track 76 and a focused line of light from an element 78 move atconstant speed with respect to the detector array 79, each detectorelement outputs a sinusoidally varying signal, with the respectivesignals from detectors 81 and 83 being offset from each other by 90degrees. As shown, the detector array 79 may include additional pairs ofdetectors such as detectors 85 and 87.

Subencoder 5: Another coarse track subencoder uses a track 80 shown inFIG. 10. This coarse track 80 is a simple 50:50 duty cycle grating,approximately 32 times more coarse than fine track 44. In theillustrated example, the coarse track 80 has a period of 640 microns.This track is also preferably used with a sinusoidal detector such asthe detector array 79 of FIG. 9.

Subencoder 6: Yet another embodiment of a coarse track subencoderutilizes a sinuous cylindrical lens to convert along-track scaledisplacement into a measurable cross-track light stripe displacement.FIG. 11 is a schematic illustration of this subencoder. The subencoderis shown operating in transmissive mode for clarity, and the scale 14has been anamorphically distorted to illustrate multiple sinuous cycles.The scale 14 includes a sinuous cylindrical lens DOE 89 extending thefull length of the scale 14. The axis of the lens is sinuous; that is,the axis of the lens is not a straight line parallel to the along-trackdirection, but rather is a sinusoidal curve extending in the along-trackdirection.

In operation as a coarse track, a portion 82 of the sinuous cylindricalDOE lens 89 is illuminated by a spatially coherent source in a sourceassembly 14A in the illustrated transmissive configuration. Theilluminated portion 82 is short compared to the period, P, of thesinuous function. Again it should be noted that in FIG. 11 the scale 14and therefore the DOE 89 have been anamorphically distorted to make theperiod P appear much shorter than actual. On an actual scale, theilluminated portion 82 appears generally horizontal.

The illuminated portion 82 of the DOE cylindrical lens 89 forms a lineimage 84 of the source on a detector 56 in the detector assembly 10B,the focal length of the DOE 89 having been designed to performapproximate 1:1 imaging at a source distance equal to thescale-to-detector assembly separation. The line image approximates aline segment whose length is proportional to the length of theilluminated region 82. The line segment is generally parallel to thealong-track direction and has a cross-track position proportional to thecross-track displacement of the axis of the DOE 89, which naturallysweeps back and forth in the Y direction as the X position of the scale14 changes. FIG. 11 illustrates with a dotted line 86 the image that iscreated when the corresponding portions of the extended, sinuouscylindrical lens DOE 89 are located in the region of illumination. Ofcourse, the line image 86 is a direct mapping of the sinuous DOE 89.Thus, as the scale moves in the along-track direction, the line segmentsweeps back and forth in the cross-track direction.

This subencoder uses a line tracking detector configuration to estimatethe cross-track position of the focused line segment. The QSD 66 of FIG.7 is suitable, as is a sharkstooth shaped detector (SSD) 56 such asillustrated in FIG. 6. The SSD 56 includes two sets of complementarytriangular photosensitive regions 58 and 60. Typically each triangle iselongated in the cross-track direction, and multiple triangular areasare arrayed next to each other in the along-track direction. The regions58 and 60 are oriented in opposing directions and are positioned to forma single interdigitated SSD 56. In the signal processing for the SSD 56,the position estimate is proportional to the difference of the signalsfrom positive regions 60 and negative regions 58, normalized by theirsum.

In a subencoder using the elongated sinuous DOE 89, it is not feasibleto perform quadrature sampling of the light pattern from the DOE 89 at asingle location. Two alternative approaches may be used. A second DOEcan be added that is offset from the first DOE 89 by one-quarter of acycle, and these two DOEs can be sampled by corresponding detectors at asingle point. Alternatively, a single DOE such as DOE 89 can be usedwith detectors separated by one-quarter of a cycle.

Other subencoders: Other coarse track subencoders may utilize othersensing technologies to produce sinusoidally varying signals. Forexample, magnets or magnet arrays may be used with magnetic sensors suchas, for example, commercially available Hall effect sensors and sensorarrays. Such subencoders can be combined with optical subencoders for ahybrid approach. This may be beneficial, for example, when opticalsubencoders are the best choice for the high resolution tracks, andmagnetic methods are best for the coarse information. It is understood,however, that magnetic subencoders could be used for the high frequencytracks or in an all magnetic design.

Reference Track: Several of the incremental subencoders that can be usedin the absolute encoder are designed to convert along-track scale motioninto cross-track measurable signals. However, any cross-track scalemotion will also appear as crosstalk error in these measurements. Whilea small degree of crosstalk may be tolerable is some applications, inmany applications it is desirable to measure and compensate for thiscrosstalk error. The scale 14 in the preferred embodiment of theabsolute encoder incorporates a reference track 46 (FIG. 5) to provide ameasure of scale cross-track motion. This measure can be used inprocessor 20 to eliminate crosstalk error.

As shown in FIG. 5, in one embodiment the reference track 46 is anextended cylindrical DOE. The axis of the cylinder is orientedsubstantially parallel to the along-track direction and the DOE extendsfor the entire operational length of scale 14.

In operation, a portion of the extended cylindrical DOE lens 46 isilluminated by the spatially coherent source in sensor apparatus 10.That portion of the lens forms a line image of the source back on adetector in the sensor apparatus 10. The focal length of the DOE 46 ischosen to perform approximate 1:1 imaging at a source distance equal tothe scale-to-detector assembly separation. The line image approximates aline segment whose length is proportional to the size of theillumination region. The line segment is substantially parallel to thealong-track direction and has a cross-track position proportional to thecross-track displacement of scale 14 relative to sensor apparatus 10.Thus, any motions of the scale in the cross-track direction moves theline segment back and forth in the cross-track direction.

A line tracking detector configuration estimates the cross-trackposition of the focused line segment. Both the QSD 66, illustrated inFIG. 7, and the sharkstooth shaped detector (SSD) 56, illustrated inFIG. 6 are suitable detectors.

As has been mentioned, multiple incremental subencoders are combinedwith an electronic processor 20 that estimates the absolute position ofthe scale 14 based only on the immediately available incrementalsubencoder signals. The process that combines the incremental subencodersignals into a single encoder position word is called “linking.” Thisprocess ensures that the encoder counts monotonically and thatultimately the accuracy of the encoder is dependent only on that of thefinest subencoder track.

Tracks may be linked in pairs, starting with the linking between thehighest frequency track and the next coarsest track. This operationproduces a corrected coarse track, which is used for the linking to thenext coarser track. This process can be cascaded as necessary to thevery coarsest track, using the corrected result from each linkingoperation to perform the link to the next coarser track. The correctedinformation from each of the coarse tracks, when combined with theinformation from the finest track, produces the encoder's outputposition word.

More specifically, FIG. 12 illustrates how linking is accomplished for agiven pair of tracks. Although in FIG. 12 these tracks are referred toas FT and CT, it will be appreciated that the same process can becarried out on other pairs of tracks, such as pairs of coarse tracksCTn, or a physical track and the (mathematical) result of a previousiteration of linking, as well. In step 88, the position value isgenerated for each of the subencoders. Depending on the subencodingmethod, this may involve digitizing the sine and cosine signals andcalculating the arctangent, as described above. Waveforms showing theposition values as a function of encoder position are shown as FT and CTin FIG. 13. It will be observed that they form a quantized ramp orsawtooth function. The fine track FT has the relatively high frequencyramp function, and the coarse track CT has a lower frequency ramp.Fine-grain quantization is omitted from FIG. 13 for clarity.

Referring again to FIG. 12, in step 90 the calculated FT and CT positionvalues are combined to create a modified CT value. The purpose of thiscombining is to create modified CT values that transition from one valueto the next in phase and synchronism with the transitions of the FTvalues (thus transferring the accuracy of FT to CT). The merginggenerally involves scaling the CT value to account for its greatersignificance, algebraically combining the FT value and the scaled CTvalue, and filtering the result to effectively remove the originaltransitions of CT.

In step 92 the calculated FT value is combined with the most significantportion of the modified CT value to create a combined value thatunambiguously represents the encoder position to the resolution of FT,modulo the period of CT.

The operations of FIG. 12 are illustrated with reference to thewaveforms of FIG. 13. For clarity, a simplified version is shown inwhich there are four periods of FT in each period of CT. In FIG. 13, theoutput of each track is shown as a ramp whose period is equal to theperiod of the track. Within each cycle, the phase (or position word)begins at zero and increases to a maximum value of 2^(M)−1 at the end ofthe period, where M is the number of bits of interpolation resolution.

The interpolation resolution of CT is chosen such that the leastsignificant part of each CT value “overlaps” with the most significantpart of the FT values. That is, the overlapping parts representnominally the same incremental position information. As described below,the number of overlapping bits is dictated in part by the amount ofuncertainty in the phase relationship of the tracks. In FIG. 13, themost-significant, non-overlapping part of CT is shown as “CT_(MSB)”. Asshown, this most significant part of CT appears as a staircase with anindeterminate phase offset with respect to the FT cycle boundaries. IfCT were perfectly aligned with FT such that all its bits transitioned inphase with corresponding bits of FT, then it would be a simple matter toconcatenate the CT_(MSB) value with the FT value to arrive at afull-resolution position value modulo the period of CT. The result ofsuch a hypothetical operation is shown as “Ideal [CT_(MSB)][FT]” in FIG.13. However, due to their random phase relationship, an actualcombination of these values might appear as labeled “Actual[CT_(MSB)][FT]” in FIG. 13—it would have a periodic glitch in thevicinity of the FT period boundaries. Thus CT itself is not suitable forcombining directly with FT.

For this reason, the modified CT values are created such that their mostsignificant portion has sample-to-sample transitions in precisealignment with the cycle boundaries of FT, this being shown in FIG. 13as “(Mod. CT)_(MSB)”. When these values are added to the correspondingvalues of FT, the resulting position values increase monotonicallymodulo the period of CT and have the resolution of FT (shown in FIG. 13as “[(MOD CT)_(MSB)] [FT]”). Specific examples are given below.

FIG. 14 shows the functions performed in combining step 90 of theprocess of FIG. 12. It is assumed that prior to this process, an averagephase offset between the FT and the CT has been determined in a separatecalibration operation. To determine this phase offset value, the totalrange of the scale 14 is traversed while the spacing between the coarsetrack transitions and the corresponding fine track transitions ismonitored. This may be done by comparing the fine track MSB transitionswith the transitions of the corresponding overlapping bit of the coarsetrack, and expressing the relative phase in terms of higher resolutionfine track states. This calibration need only be performed at encoderinitialization, not at each start up. Its purpose is to measure theaverage phase offset and store its value in non-volatile memory. As analternative, the calibration run may be performed on only somesub-interval of the entire scale, if such sub-interval accuratelyreflects the average phase relationship between the two tracks.

Once the average phase offset between the ramps of the two tracks hasbeen determined, in step 96 the relative phase between the coarse trackand the fine track is adjusted based on the average phase offset fromthe calibration. The objective is to maximize the smallest separationbetween the fine track MSB transitions and the corresponding coarsetrack bit transitions. This leads to an alignment such that the start ofthe coarse track ramp occurs roughly mid-way through a fine track ramp.The phase adjustment can be effected by adding a phase adjustment valueto each coarse track position value before further processing of thephase-adjusted coarse track position value, or by incorporating thephase adjustment in an intermediate “inverse fine track” value that issubsequently combined with the coarse track position value (as describedbelow with reference to FIG. 16). As an alternative, differential sineand cosine coarse track signals could be mixed to result in a shift ofthe coarse track ramp signal.

In step 98, the (potentially phase-adjusted) coarse track position valueis corrected by a value determined by the fine track position value. Onesuch correction is achieved by adding (2π−F)/TR to the coarse track,where F is the value from the finer subencoder and TR is the ratio ofthe periods of the two tracks. In the approach of FIG. 16 describedbelow, this is accomplished by adding the inverse fine track positionvalue to the coarse track position value.

After the correction value is added to the coarse track position word,this word is truncated in step 100 by discarding the least significantbits that overlap with the fine track position word. Performing thisoperation generates the corrected coarse track information, shown as(Mod CT)_(MSB) in FIG. 13. This corrected coarse track is then combinedwith the fine track bits in step 92 of FIG. 12. In one embodiment, thesevalues are combined by concatenation. The resulting encoder positionword gives the encoder position modulo the period of the coarse track.

In an encoder having a range beyond the maximum position value that canbe attained with only two tracks, the position word from the abovelinking process can be linked with a next-coarser track(s) in a similarmanner to yield a longer position word while retaining the precision ofthe fine track.

For robust linking between a given track and the next-higher-resolutiontrack, it is generally necessary that the lower frequency track beinterpolated to a resolution that is at least the same as the resolutionof the higher frequency track MSB. Using this amount of overlap (whichis referred to as “one linking bit”) results in a coarse transitionlocation tolerance range of +/− one-quarter of a fine track period.Interpolating the coarse track further improves the linking toleranceand permits lower accuracy coarse tracks and less accuratetrack-to-track phasing to be used. This relationship is given in Table 1below, in which the notation “<->” means that the inter-track phaseinaccuracy must be greater than the lower limit and less than the upperlimit.

TABLE 1 Tolerance # of linking bits (fraction of fine track period) 1−1/4 <-> +1/4 2 −1/2 <-> +1/2 3 −3/4 <-> +3/4 . . . . . . L (>1) −(1 −2^(−(L−1))) <-> +(1 − 2^(−(L−1)))

FIG. 15 shows a special case of the above algorithm in which only onelinking bit is employed. The non-ideal phase shift and variability ofthe coarse subencoder output is shown at the top. The result ofphase-shifting the coarse ramp is shown at the bottom, and the values ofthe coarse and fine linking bits are also shown.

A variation on the linking method involves a different way of handlingthe phase shifting. Instead of applying the phase shift constant to thecoarse position word in step 96, the correction of step 98 can bemodified by the phase constant determined during calibration. Forexample, when the start of the coarse track is phased with respect tothe fine track by π fine track radians, then the above correction of(2π−F)/TR is appropriate; however, if the coarse track is phased by 0fine track radians, then the algorithm would involve using (π−F)/TR forfine track values less than π, and (3π−F)/TR for fine track valuesgreater than π. The general form of the correction is MOD(π+PHI−F))/TRwhere PHI is equal to coarse-to-fine phasing.

Some encoder errors show up as phase or frequency modulation in thecoarse track signals. As examples, radial or axial runout of radial codetracks can cause such errors; similar errors can arise in linearencoders for different reasons. These result in the phase of the coarsetrack varying with respect to the fine track throughout the travelrange. With this variation, the measurement of phase during calibrationresults in the need to select an average phase shift which is acompromise over the travel range. As explained above, this average phaseshift can either be used to globally shift the coarse track positionoutput, or it can be used to determine the appropriate PHI for thealternative algorithm. In some cases, the use of an average PHI may bevery adequate. However, the alignment and accuracy tolerance rangescould be extended by using a different PHI at different points along thescale. This could be accomplished through the use of a lookup tablewhich is generated at the initial calibration run of the encoder. Theposition word of the coarsest track of the encoder would be theindependent variable of the table, with the local PHI for the coarsetrack being linked as the dependent variable. In this case, it is notnecessary to apply a global phase shift; but instead, a calibration scanwould likely be used to create the lookup table. The size of the lookuptable required is dependent on the spatial frequency of the lowfrequency error to be compensated for, and the desired improvement intolerances.

Alternatively, the calibration scan can be used to create a moreconventional lookup table to simply correct the coarse tracks andgenerate more accurate coarse track position word ramps for use in thelinking process. In this case, the scale would be moved through its fullrange using the finest track in incremental mode. During that movement,the coarse position words would be compared against their expectedvalues using the accumulated position word from the finest track as thereference. The expected values would be the dependent variable of thetable, with the corresponding position word of some coarse track beingused as the independent variable. The coarse track used for theindependent variable could be the one being corrected or a lowerfrequency track, perhaps even the coarsest track; the selection of thetrack to use is dependent on the frequencies of the errors to becorrected.

FIG. 16 illustrates a specific implementation of the functions of FIG.14. This description employs an index variable “i” to specificallyindicate the discrete samples that are obtained of the signalsrepresenting the tracks FT and CT. In the description of this processbelow, reference is also made to the waveform diagrams of FIG. 17.

In step 104 of FIG. 16, the sample FT(i) is subtracted from a phaseconstant PHI, which may be calculated in a calibration operation in thesame manner described above. The result of this subtraction is calledFTinv(i). As can be seen in FIG. 17, the waveform for FTinv has the sameperiod as FT, but within each period it slopes in the oppositedirection.

In step 106, a value called “rough step” RS(i) is calculated by addingFTinv(i) to the sampled value of CT (denoted CT(i)) multiplied by thetrack ratio TR. The multiplication effects a scaling that is necessaryto account for the greater period of CT on the scale. If the period ofCT is 32 times greater than the period of FT, for example, then TR isequal to 32. The scaled CT is shown in FIG. 17 with the label TR*CT. Asshown, it is a ramp having a period and amplitude of TR times the periodand amplitude of FT. It will also be observed that this ramp isgenerally fairly noisy, i.e., it is not a smooth linear ramp, which isdue in part to the scaling by TR that multiplies noise along withdesired signal. The signal RS is also shown in FIG. 17. It has agenerally staircase shape, with the transitions between steps occurringat the cycle boundaries of FT. However, due to the noise of TR*CT, thesteps themselves are not flat, but rather contain some noise as well. Aslong as this noise is within an acceptable limit, it can be filtered outas discussed below to create a smooth staircase function that can beused as the upper bits of the linked position value.

It will be noted that in FIG. 17, the initial part of the RS waveformhas an amplitude above a value labeled MAX, which is the maximum valuethat the sum of FT and (TR*CT) should be. This is a case of mathematicaloverflow—the amplitude in this region is a form of “wraparound” that isdealt with in a subsequent processing step as described below.

In step 108 of FIG. 16, a value called “smooth step” SS(i) is calculatedby applying a smoothing function SF to the value RS(i). Generally, SFmust be such that it eliminates the noise on RS while preserving thelocations of the step transitions. In one embodiment, SF may be realizedby a set of ranges or brackets and a comparison function, as illustratedin Table 2 below. This SF effects the truncation of step 100 of FIG. 14.

TABLE 2 Bracket Operation 0 ≧ RS(i) > B₁ SS(i) = 0 B₁ ≧ RS(i) > B₂ SS(i)= B₁ B₂ ≧ RS(i) > B₃ SS(i) = B₂ . . . . . . B_(J−1) ≧ RS(i) > B_(J)SS(i) = B_(J−1)

The values B_(j) in the above table are integer multiples of the numberof samples in each period of FT. Thus if FT is interpolated to a depthof 10 bits, for example, then appropriate values for {B_(j)} are {1024,2048, . . . }, and the number of brackets is equal to the track ratioTR.

In addition to the above brackets, the existence of an overflow orunderflow condition is also detected and corrected. This is done bydetermining whether the value of RS(i) is greater than MAX or less thanzero. When RS(i) is greater than MAX, it is replaced with (RS(i)−MAX)before the above bracketing is applied. Similarly, if the value of RS(i)is less than zero, it is replaced with (RS(i)+MAX) before the bracketingis applied. In FIG. 17, this process is responsible for moving thedownward transition at the beginning of the smooth step (SS) waveforminto alignment with corresponding transitions of FT and FTinv.

The resulting smooth step (SS) waveform is shown in FIG. 17. It has steptransitions in the same locations as FT and FTinv. Unlike in RS, eachstep in SS is flat. It will be observed that the SS waveform is the sameas the (Mod CT)_(MSB) waveform of FIG. 13, and is likewise suitable tobe concatenated with FT to form the linked position value. The result ofsuch concatenation is shown in FIG. 17 as CT′.

As described above, an absolute encoder can be realized by employing aset of successively coarser tracks CT₁, CT₂, . . . , CT_(N) andrepeatedly linking adjacent pairs of tracks until the full absoluteposition value has been calculated. It is also possible, in a mannerdescribed below, to achieve the same range and resolution in an encoderwithout the need for the very coarsest physical tracks. Such an approachhas desirable benefits, including smaller scale size and avoidingsensing difficulties associated with very long-period grating patterns.

FIG. 18 illustrates the concept generally. Two coarse tracks havingslightly unequal periods are formed on the scale 14. The signals fromthese two tracks are processed such that a mathematical track called a“beat track” BT is created within the processor 20. The period of BT canbe selected to be much greater than, but precisely related to, theperiods of CT₁ and CT₂. Moreover, the cycle boundaries of BT occurprecisely with respect to CT₁ and CT₂ such that BT can be linked witheither track to form a linked position word that gives absolute encoderposition modulo the period of BT. Thus, a long-period coarse track canbe realized without the need to actually include a physical long-periodcoarse track on the scale 14.

FIG. 19 depicts a scheme for generating a 25-bit absolute position valueusing one fine track, three similar-period coarse tracks and beattracks. The fine track FT is interpolated to 10 bits, which form theleast significant bits of the position word. Three coarse tracks CT₁,CT₂ and CT₃ having track ratios with FT of 32:1, 33:1 and 34:1respectively are also formed on the scale 14. Each of these coarsetracks has a respective value denoted “cycles per turn” (CPT) associatedwith it. CPT is generally associated with rotary encoders, for which itrepresents the number of periods of the track over one revolution. Withrespect to linear encoders, the term CPT is used herein to represent thenumber of periods of the track over the entire length of the encoder. Inthe example of FIG. 19, these CPT values are 561, 544 and 528respectively, which correspond to a linear scale length of about 36 cm.if the period of FT is 20 microns.

Tracks CT₁ and CT₂ are used to form a first beat track BT₁, and tracksCT₂ and CT₃ are used to form a second beat track BT₂. BT₁, has 17 cyclesper turn, and it has track ratios of 33:1 and 32:1 with CT₁ and CT₂respectively. BT₂ has 16 cycles per turn, and it has track ratios of34:1 and 33:1 with CT₂ and CT₃ respectively. Tracks BT₁ and BT₂ are usedto form a third beat track BT₃, which has 1 cycle per turn and trackratios of 17:1 and 16:1 with BT₁ and BT₂ respectively. The finalposition word has components of tracks FT, CT3, BT2 and BT3 (shownencircled). In the assumed case of a 20-micron FT period, this positionword represents a position over a 36 cm. range to a resolution ofapproximately 20 nm. It should be noted that other combinations of thevarious tracks may be used, such as (FT, CT2, BT1 and BT3).

FIG. 20 illustrates a process for realizing the scheme of FIG. 19. Instep 110, the fine track FT is linked to each of CT₁, CT₂ and CT₃, usingfor example one of the above-described linking procedures. Out of thisprocess come intermediate linked tracks CT₁′, CT₂′ and CT₃′.

In step 112, the beat tracks BT₁ and BT₂ are calculated as follows:BT ₁=(33*CT ₁′)−(32*CT ₂′)BT ₂=(34*CT ₂′)−(33*CT ₃′)

The scaling of the operands in the above calculations should be noted.This achieves two important goals. First, it imparts the properamplitude to the beat tracks. It also avoids an undesirable cancellationof the FT component, which is common to CT₁′ and CT₂′. If these trackswere to be subtracted directly, the FT component would be cancelled out,removing the important FT timing information from the new beat tracks.Such cancellation is avoided when the values of CT₁′ and CT₂′ are scaledbefore performing the subtraction.

In step 114, linked beat tracks BT₁′ and BT₂′ are created by linking BT₁and BT₂ with linked coarse tracks CT₂′ and CT₃′ respectively.

In step 116, beat track BT₃ is calculated as follows:BT ₃=(17*BT ₂′)−(16*BT ₁′)

In step 118, linked beat track BT₃′ is created by linking BT₃ with CT₃′.BT₃′ is the full resolution, one CPT waveform.

Because of its “bottom-up” approach to creating the full resolution beattrack BT₃′, the process of FIG. 20 can be referred to as“bootstrapping”. It will be noted that at each level, the beat tracksare linked to a next-lower-level track before being used to create otherbeat tracks. Specifically, both BT₁ and BT₂ are linked to CT₂′ and CT₃′respectively to create BT₁′ and BT₂′, which are then beat together toform BT₃. This bootstrapping approach provides a certain degree ofrobustness that enables the encoder to provide accurate positionestimates even if the signal quality for one or more of the physicaltracks (e.g. one of the coarse tracks CT₁-CT₃) is degraded. It ispossible to omit this intermediate linking process in alternativeembodiments. That is, unlinked first-level beat tracks such as BT₁ andBT₂ (rather than linked tracks BT₁′ and BT₂′) can be used to createsecond-level beat tracks such as BT₃. This is possible because thefirst-level beat tracks are themselves formed from linked tracks (e.g.CT₁′-CT₃′), and thus already include the accuracy and resolution of FT.

Such a modified process has the benefit of requiring fewer computations,and thus can contribute to improved system performance in certainrespects. However, the performance of such a modified process may besomewhat more sensitive to degraded signals than the full bootstrappingapproach of FIG. 20. This sensitivity can be ameliorated to some extentby careful selection of the track ratios. In the embodiment of FIG. 19,for example, it is beneficial that the ratios between the coarse tracksCT_(n) and the first-level beat tracks (BT₁ and BT₂) are 32, 33 and34—it is preferable that these ratios be about 32 or less. Also, it isbeneficial that these same track ratios are close together. When thebeat tracks BT₁ and BT₂ are created from the linked coarse tracks scaledby these track ratios (step 112), much of the scaled amplitude of the FTis subtracted out, so any errors present on FT are reduced accordingly.

FIG. 21 illustrates a situation that can arise in the calculation of thebeat tracks. For example, in the calculation of beat track B₁, theresult of the operation (33*CT₁′)−(32*CT₂′) may be negative. This isshown as a downward glitch in FIG. 21. In this case, the negative valueis corrected to a corresponding positive value by adding the maximumamplitude of B₁ to it. This correction takes the following specificform:BT ₁(i)=(33*CT ₁′)−(32*CT ₂′)

-   -   IF BT₁(i)<0, then        BT ₁(i)=BT ₁(i)+BT ₁max    -   End IF

In the illustrated example, BT₁max is 1,081,344, calculated as(1024)×(32)×(33). The waveform for BT₁ as corrected is also shown inFIG. 21.

In the scheme of FIG. 19, all of the track ratios are integer values. Itmay be desirable in alternative embodiments to employ one or more coarsetracks CT that do not have an integer track ratio TR with the fine trackFT. A given application of an encoder may have a requirement for aparticular range and a particular resolution such that no set ofsuitable integer-multiple CTs can be found. In such an application itwould be beneficial to permit non-integer track ratios so that finding aset of suitable CTs is possible. However, the linking approach asdescribed above cannot be used to link track pairs having a non-integertrack ratio. A modification of the approach is required and is describedbelow.

FIG. 22 illustrates an example of such an application. The range of thescale is 13,485 cycles of the fine track period, in contrast to the17,952 cycles of the example of FIG. 19. Coarse tracks of 435 CPT, 465CPT and 496 CPT are utilized, which have respective tack ratios with thefine track of 31:1, 29:1 and 27.1875:1.

The method for linking CT3 to FT in this example is to employ a separatecalculated track that is referred to as a “virtual fine track” or VFT,as illustrated in FIG. 23. The VFT has an integer relationship with bothCT2 and CT3. In the particular example of FIG. 23, the VFT has 7,440 CPTand ratios of 16:1 and 15:1 with CT2 and CT3 respectively. The VFT iscreated by multiplying the linked signal CT₂′ by 16. Calculations foraccomplishing such multiplication are known in the art. The resultingVFT has the integer ratio of 15:1 with CT₃ and can therefore be linkedto it to form the linked signal CT₃′, which maintains all the timinginformation of FT while having a desirable non-integer period ratio withFT.

Once the linked waveform CT₃′ has been formed as described above, thebeat tracks B1, B2 and B3 and the corresponding linked waveforms can becreated in the same manner as described in the previous example.

There may be variations of the above-described techniques pertaining tothe use of linking, beat tracks, and virtual tracks. For example, a beattrack may be created out of unlinked coarse tracks, and the fine trackthen links directly up to the beat track. Following the above example,this can be expressed as B17=CT1−CT2, and B17′=B17 linked with FT. Inanother alternative, a beat track can be formed from one linked coarsetrack and an unlinked coarse track, e.g. B17=CT1′−CT2, then B17′=B17linked with either CT1′ or FT.

A track such as FT can also be linked to a virtual track such as VFT.Additionally, a virtual track can be used with other tracks to create abeat track, whether the other tracks are linked, unlinked, or virtual.

Selection of Subencoders

In this section, selection criteria for the subencoders to be used toconstitute an absolute encoder are presented. First, it is preferablethat a single compact sensor apparatus 10 be used, and therefore allsubencoders preferably operate with a common set of parameters. Forexample, all subencoders might have a scale-to-detection assemblydistance of approximately 5 millimeters. Similarly, all subencoderdetectors might have linear dimensions less than or equal to apredetermined maximum size such as 2 millimeters.

Additional considerations include the desired position resolution of theabsolute encoder (typically on the order of 0.02 microns), the totaldesired measurement range (ranging up to 3 meters for example), and theexpected fractional resolution of each subencoder candidate (that is,what fraction of a period can be resolved).

These multiple criteria may best be explained with reference to theexemplary encoder illustrated in FIG. 1, the set of tracks illustratedschematically in FIG. 5, and the detectors illustrated in FIGS. 6 and 7.The fine track 44 is a 20 micron period, square wave reflective grating.This grating is well suited for use in a Talbot interference encoder inwhich a VCSEL source is located on a common substrate with a fringedetector, with the common substrate located about 5 millimeters from thescale. This type of incremental encoder has been demonstrated to provideat least 0.02 micron resolution when used with an interdigitated, 4-bindetector such as detector 50.

If the absolute encoder has a total range of, say 0.65 meters (˜650,000microns), then the coarse track subencoders must, in combination,provide about 15 bits of range (that is, 2^15≈650000/20). Since it isrelatively easy to provide a track ratio of 32 (5 bits), it appears thatthree coarse subencoders providing 5-bits of range each will suffice (ifthe cascaded approach is utilized rather than the beat track approach,as is presumed in this example). Thus, coarse track 42 has a period of640 microns (32×20 microns); coarse track 40 has a period of 20.48millimeters (32×0.64 millimeters); and coarse track 38 has a period of655.36 millimeters (32×20.48 millimeters).

Coarse track 42 is formed by modulating the edge of fine track 44.Alternative tracks for the 640 micron period track are a repeated indextrack 76 (FIG. 8) or a coarse 50:50 duty cycle grating 80 (FIG. 10).Each of these tracks can be sensed by a detector such as detector array79, and none of these tracks are sensitive to cross-track motion.

The second and third coarse tracks, track 40 and track 38, are bothsloped grating tracks. This type of subencoder converts relatively longrepeat periods (20.48 millimeters and 655.36 millimeters, for example),which are hard to detect with a small (˜2 millimeter) detector, intomotions which repeat over a much shorter distance (400 microns at thedetector plane) and which are amenable to detection with a smalldetector. Tracks 40, 38 are matched with QSD arrays 66 each of whichmeets the 2 millimeter or smaller criterion.

The final track in this example is reference track 46, which is matchedwith SSD 56. Reference track 46 is included to correct for thecross-track sensitivity of track 40 and track 38.

In this example, an additional SSD 62 (see FIG. 6), is optionallyincluded. The addition of a second SSD to measure the cross-trackposition of reference track 46 provides an angular alignment aid. Thatis, the two SSDs 56 and 62 will measure an identical cross-trackposition for reference track 46 when the sensor apparatus 10 is parallelto reference track 46.

Although the examples in the foregoing description have utilizedfixed-point mathematics, in alternative embodiments it may be necessaryor convenient to utilize floating-point mathematics instead. All theprocesses described herein can be implemented in an analogous fashionusing floating-point calculations.

Also, while the above description focuses on optical encoders inparticular, it will be appreciated that the presently disclosedtechniques may be utilized in position encoders of other types,including for example electrical or magnetic position encoders.

Those skilled in the art will appreciate that embodiments and variationsof the present invention other than those explicitly disclosed hereinare possible. It is to be understood that modifications to the methodsand apparatus disclosed herein are possible while still achieving theobjectives of the invention, and such modifications and variations arewithin the scope of this invention. Accordingly, the scope of thepresent invention is not to be limited by the foregoing description ofembodiments of the invention, but rather only by the claims appearingbelow.

1. A position encoder, comprising: a scale including a periodic firsttrack and two or more periodic second tracks operative to generatecorresponding periodic first and second energy patterns, the secondtracks having distinct but generally similar periods; detector circuitryoperative in response to the periodic energy patterns to generatecorresponding sets of analog signals, the analog signals within each setrepresenting amplitudes of the corresponding energy pattern atpredetermined spatial locations; and processing circuitry operative inresponse to the sets of analog signals: (i) to generate linked positionestimates, each linked position estimate representing a sampled phase ofa corresponding one of the second energy patterns linked to a sampledphase of the first energy pattern; and (ii) to generate one or more beattrack estimates by an algebraic combination of the linked positionestimates such that each beat track estimate represents a correspondingbeat track having a beat period greater than the period of the secondtracks from whose linked position estimates the beat track estimates aregenerated, wherein the period of a predetermined one of the secondtracks has a non-integer ratio with the period of the first track, andwherein the processing circuitry is further operative: (iii) to generatea virtual track by applying a frequency-dividing function to the linkedposition estimates for another of the second tracks, such that theperiod of the virtual track has an integer ratio with the period of thepredetermined second track; and (iv) to link the predetermined secondtrack with the virtual track.
 2. A position encoder, comprising: a scaleincluding a periodic first track and two or more periodic second tracksoperative to generate corresponding periodic first and second energypatterns, the second tracks having distinct but generally similarperiods; detector circuitry operative in response to the periodic energypatterns to generate corresponding sets of analog signals, the analogsignals within each set representing amplitudes of the correspondingenergy pattern at predetermined spatial locations; and processingcircuitry operative in response to the sets of analog signals: (i) togenerate linked position estimates, each linked position estimaterepresenting a sampled phase of a corresponding one of the second energypatterns linked to a sampled phase of the first energy pattern; and (ii)to generate one or more beat track estimates by an algebraic combinationof the linked position estimates such that each beat track estimaterepresents a corresponding beat track having a beat period greater thanthe period of the second tracks from whose linked position estimates thebeat track estimates are generated, wherein: the period of each of thesecond tracks exceeds the period of the first track by a correspondingtrack ratio; and the processing circuitry is operative when generatingeach of the linked position estimates to: (iii) generate first andsecond position sample values of the first and corresponding secondtrack respectively, each position sample value being an incrementalposition sample value within a period of the respective track, thesecond position sample value having sufficient resolution that apredetermined number of least significant digits of the second positionsample value are overlapping digits representing nominally the sameposition information as corresponding most significant digits of thefirst position sample value, the predetermined number being determinedby the magnitude of uncertainty of a spatial phase relationship betweenthe first and corresponding second track over a predetermined portionthereof; (iv) scale the second position sample value by a numbercorresponding to the corresponding track ratio to form a second positionestimate value having the overlapping digits occupying the same digitpositions as the corresponding most significant digits of the firstposition sample value, (v) subtract the first position sample value fromthe second position estimate to create a corrected second positionestimate; and (vi) combine the first position sample value with anon-overlapping most significant part of the corrected second positionestimate.
 3. A position encoder according to claim 2 wherein the scaleis an optical scale, the first and second tracks comprise respectivearrays of optical elements, the periodic energy patterns are opticalenergy patterns, and the detector circuitry comprises optical detectorcircuitry.
 4. A position encoder, comprising: a scale including aperiodic first track and two or more periodic second tracks operative togenerate corresponding periodic first and second energy patterns, thesecond tracks having distinct but generally similar periods; detectorcircuitry operative in response to the periodic energy patterns togenerate corresponding sets of analog signals, the analog signals withineach set representing amplitudes of the corresponding energy pattern atpredetermined spatial locations; and processing circuitry operative inresponse to the sets of analog signals: (i) to generate linked positionestimates, each linked position estimate representing a sampled phase ofa corresponding one of the second energy patterns linked to a sampledphase of the first energy pattern; and (ii) to generate one or more beattrack estimates by an algebraic combination of the linked positionestimates such that each beat track estimate represents a correspondingbeat track having a beat period greater than the period of the secondtracks from whose linked position estimates the beat track estimates aregenerated, wherein the first track comprises a linear array of spacedrectangular regions, and one of the second tracks comprises a spatiallymodulated edge portion of the first track.
 5. A position encoderaccording to claim 4 wherein the detector circuitry comprises first andsecond linear arrays of photo detector elements, the first array havinga fine pitch corresponding to the period of the first track and thesecond array having a coarser pitch corresponding to the period of acorresponding one of the second tracks.
 6. A position encoder accordingto claim 5 wherein each of the arrays of photo detector elementsconstitutes a quadrature detector.
 7. A position encoder, comprising: ascale including a periodic first track and two or more periodic secondtracks operative to generate corresponding periodic first and secondenergy patterns, the second tracks having distinct but generally similarperiods; detector circuitry operative in response to the periodic energypatterns to generate corresponding sets of analog signals, the analogsignals within each set representing amplitudes of the correspondingenergy pattern at predetermined spatial locations; and processingcircuitry operative in response to the sets of analog signals: (i) togenerate linked position estimates, each linked position estimaterepresenting a sampled phase of a corresponding one of the second energypatterns linked to a sampled phase of the first energy pattern; and (ii)to generate one or more beat track estimates by an algebraic combinationof the linked position estimates such that each beat track estimaterepresents a corresponding beat track having a beat period greater thanthe period of the second tracks from whose linked position estimates thebeat track estimates are generated, having at least two of the beattracks constituting first-level beat tracks, and wherein the processingcircuitry is further operative to form a second-level beat track by analgebraic combination of the beat tracks such that the second-level beattrack has a beat frequency equal to a difference between the frequenciesof the first and second beat tracks.
 8. A position encoder according toclaim 7 wherein the processing circuitry is further operative to (i)link each of the beat track estimates with a predetermined one of thelinked position estimates so as to generate respective linked beatestimates representing first-level linked beat tracks, and (ii) form asecond-level beat track by an algebraic combination of the first-levellinked beat tracks such that the second-level beat track has a beatfrequency equal to a difference between the respective frequencies ofthe first-level linked beat tracks.
 9. A position encoder according toclaim 8 wherein the processing circuitry is further operative to linkthe second-level beat track and a predetermined one of the first-levellinked beat tracks.